Problem: The sum of $6$ consecutive integers is $501$. What is the first number in this sequence?
Answer: Call the first number in the sequence $x$ The next integer in the sequence is $x + 1$ The sum of the $6$ consecutive integers is: $x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4)+ (x + 5) = 501$ $6x + 15= 501$ $6x = 486$ $x = 81$ Thus, the first number is $81$.